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This paper presents an approximate decomposition method for the performance evaluation of non-homogeneous fabrication/assembly (F/A) systems with multiple failure modes, finite buffers, and a fixed assembly proportion. First, we introduce a mixed flow combined with fund flow and material flow to convert an F/A system to a virtual transfer line. Then, we decompose the virtual transfer line into several two-machine lines and establish a continuous decomposition model. To tackle the new emerging characteristics of the F/A system, we propose an F/A decomposition algorithm (FADA) for solving this model and obtain the throughput and buffer level of the F/A system to evaluate system performance. Also, we demonstrate the validity of the proposed model and algorithmby comparing with the results of simulation-based method and completion time approximation (CTA)-based method. Finally, we analyze the impact of several key parameters, including failure rates, repair rates, and buffer capacities, on the performance of the F/A system. The results show that our analytical method outperforms the existing methods and can help production managers to evaluate the system performance, analyze the possible modifications, and further find the best performance improvement of such F/A systems. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model of steady-state reaction-diffusion (RD) model for estimating the concentration of species is discussed. We have applied a new wavelet-based operational matrix of derivative method to obtain the approximate solutions for nonlinear RDEs. The proposed method is a powerful and easy-to-use analytical tool for linear and nonlinear problems. Some illustrative examples are given to validate our results with exact solutions. Satisfactory agreement with the exact solution is noticed. Moreover, the use of Legendre wavelets is found to be simple, accurate, efficient and requires small computation costs. [ABSTRACT FROM AUTHOR]

In this paper, as an extension of a previous study, an improved approximation for the Gaussian Q-function is presented. The nonlinear least squares algorithm is employed to optimize the coefficients of the proposed approximation. The accuracy of the presented approximation is evaluated using extensive computer simulations. Results show that the proposed approximation has superior accuracy in high arguments' region when compared to the performance of other approaches introduced in the literature. [ABSTRACT FROM AUTHOR]

In this paper we propose a numerical procedure for the prediction of capillary forces in polydisperse granular assemblies at a degree of moisture content that corresponds to the so-called pendular regime. The capillary force model is adopted within the Laplace-Young framework with a toroidal approximation of the liquid bridge geometry. Governing equations are first derived in a form that highlights the role of intrinsic parameters such as inter-particle separation distance, ratio of particle radii and liquid volume. A proper scaling of these equations is adopted so that the solution applies to any particle pair configuration. Numerical integration algorithms are provided in a way that facilitates implementations in macroscopic procedures for computer simulations. A qualitative evaluation is undertaken to highlight model predictions of the effects on capillary force of various intrinsic parameters that characterise the particle pair and liquid bridge. The model is validated against the experimental results provided by Willet et al. (Langmuir 16:9396-9405, ) for a wide range of liquid volumes and particle-pair polydispersity. [ABSTRACT FROM AUTHOR]